There are several form
of energy and some related concepts.To
begin let us examine mechanical systems. Basically I am talking about blocks
and balls. In particular we will start with a mass and a spring.

Energy of motion:
Kinetic Energy

Energy is a simple
number you can add to it or subtract it from an object.Basically the amount of KE an object contains
is proportional to its mass and how fast it is moving.So when trying to figure out how much KE
energy an object has you need to consider both factors. A car and a tennis ball
have very different masses but they can both have the same KE but the tennis
ball must be moving much faster than the car.

mass

v

KE

mass

v

KE

kg

m/s

mph

ftpmin

J

kg

m/s

mph

ftpmin

J

0.057

1.0

2.2

18.3

0.03

1000.00

0.01

0.02

0.14

0.03

5.0

11.2

91.4

0.71

0.04

0.08

0.69

0.7

10.0

22.4

182.9

2.9

0.08

0.17

1.4

2.9

100.0

223.7

1828.8

285.0

0.8

1.7

13.8

285.0

343.0

767.3

6272.8

3353.0

2.6

5.8

47.4

3353.0

The behavior and
relationships are straightforward but foreing so we
will consider money as an analog to energy.

KE is the energy an
object “carries” è Money in one’s wallet.

PE:potential
energy

This is a different
form of energy. The book points out that the name could be confusing because it
sounds like pseudo energy but this
is a real from of energy. One type of potential energy is SPE: spring potential
energy.

xè stretched (compressed) distance from the
relaxed state

Here we see that the
more you stretch (compress) the spring the more energy is present in the
spring.

To continue with our
model we would like to add another form of money. We will consider money in our
checking account as the analog to the SPE.

To apply this model we
know that our total amount of money is the sum of the money in our wallet plus
the amount in our checking account. These are two forms ofmoney in the same way that we have two
forms of energy.Lets add one more.

GPE: gravitational PE

hè is the height of the object

For simplicity we will
choose the lowest point in a problem to be h=0.We should become comfortable with the formula. Since this is a product
of three values with one value g being a constant we can easily see how energy
changes with mass m and height h. The higher something is the more energy it
contains and the heavier it is the more energy it contains.

Gravity is sort of an
invisible form of energy so we need to make it more real.The way the energy is stored is by adding
energy to the gravitational field.There
is a real place to put the energy.Although the formula is different, you can imagine an invisible spring
being stretched as you lift something up. There is energy available or present
in a spring when it is compressed. There is gravitational energy present due to
the attraction of masses. In order to build a configuration of objects when
gravity is involved you need to put energy into the gravitational field.The amount of energy is related to how far
the objects are apart.For our systems
of blocks and balls, people and cars on the earth the problem simplifies to h,
the height of an object.

ASIDE h=0

In terms of calculation
the zero point for potential energy is not critical.If you could borrow money from your
checking account then you would not be limited by a zero amount as you could
keep extracting money it would just be negative or debt.For gravity on the earths surface we can be
considering the energy for a ball dropping and make the floor h=0. If we
dropped the ball out the window it would fall to a negative value of h but
the energy associated with the fall would be positive.In some sense we can keep extracting energy
as we go to negative heights and the chosen h=0 is irrelevant in terms of how
much energy I have obtained by falling.

This may seem like a
tricky point but we do this all the time.We typically measure height wrt the most
convenient reference point and not in an absolute sense. In all of the
quantities below its really the change or difference
in location that is the relevant. The convenient location for your zero point
is usually obvious but not required.Establishing the locations of pictures and shelving in a room I could
measure the height wrt the floor or the ceiling. As
long as the person putting up the pictures and shelves understood the room
would be layed out correctly.

SKI AREAS

height
from base or lodge

MY HEIGHT

from
my feet

DESK

from
the floor

HARRISONBURG

from
sea level

EARTH

from
the sun

SOLAR SYSTEM

from
center of milky way

To continue our model
we simply add another checking account.Since this is potential energy we will just open a new account in a
different bank.

Now that we have
identified three types of energy and three locations for money we can address
the question of transfer.Energy can be
transferred from one form to the other. Your money can be transferred from one
location to another.We will simply
imagine one ATM machine that does the work. I can take money from my wallet and
deposit it or retrieve it from a checking account.

Work: Method of energy
transfer

work
is force through a distance

The formula is
complicated by the requirement that in order to do work you need to move in the
direction of the force.To encapsulate
this idea I suggest you consider throwing and catching a baseball. Here you
push the ball in the direction the ball is moving and move your hand along the
path of the ball to add energy to the ball and in catching you push opposite
the motion along the path.This is all
there is to the interpretation of the formula if the force and motion are
parallel. If they are perpendicular then no work is done.This is counterintuitive because we
experience this differently. Standing and holding an object seems like work and
carrying an object seems like work but these actions do not give any energy to
the object. If we push something along its motion it speeds up.If the object doesn’t move in the direction that
we are pushing we do not do work.

At this point we will
introduce a second method of energy transfer HEAT.We will discuss it in more detail later but
identifying it as transfer rather than energy is important so we sill include
it in our table

KE

SPE

GPE

WORK

HEAT

Energy of motion

Spring PE

gravitational

Transfer energy

Energy transfer
involving temperature

Money in Wallet

Money in checking
account

BANK: spring

Checking

BANK: grav.

ATM moves money
from A to B

Different ATM to
move money around

I like this model because it clearly identifies the
difference between work, heat and energy.If you are isolated then you simply add up all the energy and ignore the
transfer.The relevant question is how
much money do I have.A person can
chart, of course, the details and describe the various processes.I deposited $10 in the bank by taking $10
from my wallet.A mass spring system may
be isolated and then the energy goes from KEèPEèKEèPE ….In the
compression the mass does work in the direction of the spring thereby W(mass èsp) adds energy to the
spring.The spring is pushing opposite
the mass so W(sp =>
mass)takes energy out of the mass and
it slows down.So if you want to keep
track of the energy and its specific location you will need to look at the
transfer or work.

Energy is conserved so whatever is transferred out of one
location or form is placed in another location or form.This of course is similar to money at least
for ordinary people.We can’t make money
and it basically moves around without changing, so it is conserved.

Just as in the case of money it is often important to
isolate certain types of energy and keep track of them.I am very concerned with my total
wealth.So in order to keep track of the
relevant information I need to have a way to add money to my wealth by taking
it from some other location EARNand also to SPEND money that is
subtracted from my wealth.

For energy we do not
need to introduce a new concept just keep track of the specific types of energy
transfer.We define work by external
forces.These are forces that act on
that add or subtract from our energy.As
noted earlier for every force that we exert on an object there is an equal and
opposite for (3rd law).So we
don’t double count.Our spending is
another person’s earnings.In figuring
out how much we have we can ask either how much did I spend or how much did the
store earn in figuring my wealth but I don’t use both.

Positive external work

Negative external work

EARN

SPEND

Something pushes an object in the direction it is moving
thereby transferring energy to the object

Now the external force opposes the motion and energy is
extracted from the object

Nothing new has really been added we are just keeping track
of the energy and isolating the system of interest.

where W represents all of the work done on the system
by external forces

For our mass spring
system we know that the energy is being removed from the system because it
slows down. The air is pushing on the ball as it moves.It always opposes the motion so energy is
being continuously removed from the ball.That energy doesn’t disappear it ends up as KE and the air moves faster
than it was moving initially.

Next concepts:

Power è Wages (spending rate)

These quantify the
rate of energy transfer or the rate of earning or spending

ØWages:$/hour

ØWage-hours = PAY

ØExamplewage=$10/hour

Ø6 wage-hours = $60

ØPower: kW = 1000 Watts= 1000J/s

ØkWh=Energy

ØExample 5 kWh

1000J/s 5h 3600s/h=18000000
J

UNITS

Joule (J)=energy =1
kg-m2/s2

calorie 1 cal=4.184 J

Physics cal = energy 1 gm water 1oC

Cal = Food calories=
1000 physics cal

Approximately1 kWh = 1000 Cal(food)

Energy
per gram

(see Physics for
Future Presidents)

object

Calories

(~Watt-hours)

Joules

Versus TNT

bullet (at sound speed- 1000 ft/s)

0.01

40

0.015

battery (auto)

0.03

125

0.05

battery (rechargeable computer)

0.1

400

0.15

battery (alkaline flashlight)

0.15

600

0.23

TNT
(the explosive trinitrotoluene)

0.65

2723

1

modern High Explosive (PETN)

1

4200

1.6

chocolate chip cookies

5

21000

8

coal

6

27000

10

butter

7

29000

11

alcohol (ethanol)

6

27000

10

gasoline

10

42000

15

natural gas (methane- CH4)

13

54000

20

hydrogen gas or liquid (H2)

26

110000

40

asteroid or meteor (30 km/sec)

100

450000

165

uranium-235

20 million

82 billion

30 million

Note: many numbers in this table have been
rounded off.

For
burning reactions (oxidation) that require the addition of oxygen the weight
of the oxygen is not included. For a cookie this reduces the C/gm to 2.5. TNT is a self contained
reaction no external matter required.

Burning
gasoline results in carbon dioxide and water vapor few other gases.No appreciable solid residue to vent.